Buyer-Supplier Games: Core Characterization and Computation

In a buyer-supplier game, a distinguished player, called the buyer, wishes to purchase some combinatorial object. A set of players, called suppliers, offer pieces of the object for sale. In this paper, we provide a transformation from most combinatorial minimization problems to buyer-supplier games; a characterization of the core of buyer-supplier games in the transferable and non-transferable utility cases; a polynomial time algorithm for optimization over the core of buyer-supplier games for which the underlying minimization problem is solvable in polynomial time; and an impossibility result showing that it is hard to distinguish core vectors if the base minimization problem is not solvable in polynomial time. We also introduce and study the concept of focus point price, which answers the question: If we are constrained to play in equilibrium, how much can we lose by playing the wrong equilibrium? ∗Supported by an MCD Fellowship from the University of Texas at Austin. †Supported by NSF Grants CCR–0310970 and ANI–0326001.